由弦对偶得到的局部化和猜想
Localization and Conjectures from String Duality
摘要：
我们描述了局部化方法，特别是函子局部化公式在弦论几个命题证明中的应用。函子局部化公式将复杂模空间上的计算推到简单模空间上。它是一般镜像公式的证明、齐次流形的基本超几何级数显式的Hori-Vafa公式的证明、Mariño-Vafa公式的证明及其推广到两个分区模拟的关键技术。我们还将讨论我们在拓扑顶点数学理论方面的发展以及ELSV公式和Witten猜想的简单局部化证明。这是我在2005年8月20 - 26日在天津举行的第23届国际理论物理微分几何方法会议上的演讲。
英文摘要：
We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli spaces to simple moduli spaces. It is a key technique in the proof of the general mirror formulas, the proof of the Hori-Vafa formulas for explicit expressions of basic hypergeometric series of homogeneous manifolds, the proof of the Mariño-Vafa formula, its generalizations to two partition analogue. We will also discuss our development of the mathematical theory of topological vertex and simple localization proofs of the ELSV formula and Witten conjecture. This is my lecture on the 23rd International Conference of Differential Geometric Methods in Theoretical Physics Tianjin, 20 - 26 August, 2005.
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